This paper proposes geometric Ricci–flow as a general model for reaction–diffusion systems and dissipative solitons in mathematical biology.

In this paper show that dissipative mechanical systems can be represented as Hamiltonian formalism. We have defined an expanded Hamiltonian function that leads to a unique conservative system for every phase flow of a dissipative mechanical system. We have demonstrated, whether the class of dissipative mechanical system has an analytical solution or not, it can be represented as an infinite num...

≥ λ||dM ||2 − λ2 (2π)(2 + ε). ∗Received by the editors October 20, 2002; accepted for publication November 26, 2002; published electronically May 12, 2003. http://www.siam.org/journals/sinum/41-2/41653.html †Department of Mathematics, Penn State University, 307 McAllister Bldg., State College, PA 16802 ([email protected]). ‡Department of Mathematics, Shanghai Normal University, 100 Guilin Road, ...

Article history: Received 29 August 2013 Received in revised form 10 December 2013 Accepted 3 February 2014 Available online 10 February 2014

In this short paper we study the problem of existence of a controlled behavior that is strictly dissipative with respect to a quadratic supply rate. The relation between strictness and the rank of a suitable qudratic differential form that couples the dissipativity properties of the hidden behavior and the orthogonal complement of the plant behavior is analyzed.

A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.

Article history: Received 2 April 2016 Received in revised form 21 July 2016 Accepted 26 July 2016 Available online 29 July 2016

Philippe Grelu,* Wonkeun Chang, Adrian Ankiewicz, Jose M. Soto-Crespo, and Nail Akhmediev Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 5209 CNRS, Université de Bourgogne, 9 Avenue A. Savary, BP 47870, Dijon CEDEX 21078, France Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies, The Australian National University, Canberra, Australian Cap...

A horizontal layer containing a miscible mixture of two fluids can produce dissipative solitons when heated from below. The physics of the system is described, and dissipative solitons are computed using numerical continuation for three distinct sets of experimentally realizable parameter values. The stability of the solutions is investigated using direct numerical integration in time and relat...